Functional Integration with an ``Automorphic'' Boundary Condition and Correlators of Third Components of Spins in the $XX$ Heisenberg Model
Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 2, pp. 285-298
Voir la notice de l'article provenant de la source Math-Net.Ru
For the generating function of static correlators of the third components of spins in the $XX$ Heisenberg model, we derive a new representation given by a combination of Gaussian functional integrals over anticommuting variables. A peculiarity of the resulting functional integral is that a part of the integration variables depend on the imaginary time automorphically: these variables are multiplied by a certain complex number under the shift of the imaginary time by the period. The other variables satisfy the standard boundary conditions of the fermionic/bosonic type. Functional integration results are represented as determinants of matrix operators. We finally evaluate the generating function of correlators and the partition function of the model in the zeta-function regularization. The consistency of the suggested functional definition is confirmed by calculating several correlation functions of the third components of spins at a nonzero temperature.
Keywords:
functional integration, $XX$ Heisenberg model, correlators, generalized zeta function.
@article{TMF_2003_136_2_a7,
author = {K. L. Malyshev},
title = {Functional {Integration} with an {``Automorphic''} {Boundary} {Condition} and {Correlators} of {Third} {Components} of {Spins} in the $XX$ {Heisenberg} {Model}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {285--298},
publisher = {mathdoc},
volume = {136},
number = {2},
year = {2003},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a7/}
}
TY - JOUR AU - K. L. Malyshev TI - Functional Integration with an ``Automorphic'' Boundary Condition and Correlators of Third Components of Spins in the $XX$ Heisenberg Model JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2003 SP - 285 EP - 298 VL - 136 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a7/ LA - ru ID - TMF_2003_136_2_a7 ER -
%0 Journal Article %A K. L. Malyshev %T Functional Integration with an ``Automorphic'' Boundary Condition and Correlators of Third Components of Spins in the $XX$ Heisenberg Model %J Teoretičeskaâ i matematičeskaâ fizika %D 2003 %P 285-298 %V 136 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a7/ %G ru %F TMF_2003_136_2_a7
K. L. Malyshev. Functional Integration with an ``Automorphic'' Boundary Condition and Correlators of Third Components of Spins in the $XX$ Heisenberg Model. Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 2, pp. 285-298. http://geodesic.mathdoc.fr/item/TMF_2003_136_2_a7/